thermodynamic_temperature¶
- astropy.units.equivalencies.thermodynamic_temperature(frequency, T_cmb=None)[source]¶
Defines the conversion between Jy/sr and “thermodynamic temperature”, \(T_{CMB}\), in Kelvins. The thermodynamic temperature is a unit very commonly used in cosmology. See eqn 8 in [1]
\(K_{CMB} \equiv I_\nu / \left(2 k \nu^2 / c^2 f(\nu) \right)\)
with \(f(\nu) = \frac{ x^2 e^x}{(e^x - 1 )^2}\) where \(x = h \nu / k T\)
- Parameters:
- frequency
Quantity
The observed
spectral
equivalentUnit
(e.g., frequency or wavelength). Must have spectral units.- T_cmb
Quantity
[:ref: ‘temperature’] orpython:None
The CMB temperature at z=0. If
None
, the default cosmology will be used to get this temperature. Must have units of temperature.
- frequency
Notes
For broad band receivers, this conversion do not hold as it highly depends on the frequency
References
[1]Planck 2013 results. IX. HFI spectral response https://arxiv.org/abs/1303.5070
Examples
Planck HFI 143 GHz:
>>> from astropy import units as u >>> from astropy.cosmology import Planck15 >>> freq = 143 * u.GHz >>> equiv = u.thermodynamic_temperature(freq, Planck15.Tcmb0) >>> (1. * u.mK).to(u.MJy / u.sr, equivalencies=equiv) <Quantity 0.37993172 MJy / sr>